To monitor events of notifications sending out failures from the external server to the notifications' recipient, login to the external server over SSH and check its mail log. For example, if the external mail server runs on Linux, grep /var/log/maillog by "recipient@example.com" and "status=deferred":

# grep recipient@example.org /var/log/maillog | grep status=deferred

Note: don't forget to replace the email address with actual notifications recipient address. The external mail server should be online for the events be logged to /var/log/maillog